(1) we introduce a randomised adaptive group Lasso to promote grouped sparsity to discover the common underlying PDE from multiple experiments. The group adaptive Lasso [1]} is known to have better asymptotic properties than the group Lasso [2]} in terms of model selection consistency. The additional randomisation we propose leads empirically to better results, especially once integrated in a stability selection loop - (2) we implement the latter into the deep learning discovery framework DeepMod (see note REF ) to perform discoveries from highly noisy datasets. Overall, our experimental results show for the first time, more generalizable PDEs can be found from multiple highly noisy datasets, by promoting grouped sparsity rather than simply performing independent model discoveries. Finally, our results suggest sharing layers across neural networks within DeepMod does not necessarily improve the inference performance.
